PIRSA:15020078

Tensor Networks from Integral Geometry

APA

Czech, B. (2015). Tensor Networks from Integral Geometry. Perimeter Institute. https://pirsa.org/15020078

MLA

Czech, Bartek. Tensor Networks from Integral Geometry. Perimeter Institute, Feb. 24, 2015, https://pirsa.org/15020078

BibTex

          @misc{ pirsa_15020078,
            doi = {},
            url = {https://pirsa.org/15020078},
            author = {Czech, Bartek},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {Tensor Networks from Integral Geometry},
            publisher = {Perimeter Institute},
            year = {2015},
            month = {feb},
            note = {PIRSA:15020078 see, \url{https://pirsa.org}}
          }
          

Abstract

The analogy between Multi-scale Entanglement Renormalization
Ansatz (MERA) and the spatial slice of three-dimensional anti-de
Sitter space (AdS3) has motivated a great interest in tensor networks
among holographers. I discuss a way to promote this analogy to a
rigorous, quantitative, and constructive relation. A key quantitative
ingredient is the way the strong subadditivity of entanglement entropy
is encoded in MERA and in a holographic spacetime. The upshot is that
the map between MERA and the spatial slice of AdS3 is mediated through
an additional integral transform. Interpreted directly, MERA is a
discretization not of the spatial slice of AdS3, but of the space of
geodesics on the spatial slice of AdS3.